assignment · 2010. 8. 20. · lots and rockets introduction to quadratic functions 1. the length...

Lots and Rockets

Introduction to Quadratic Functions

1. The length of a rectangle is 15 inches longer than its width.

a. Write an equation to represent the area of the rectangle.

b. If the width of the rectangle is 18 inches, what is the area?

c. If the length of the rectangle is 50 inches, what is the area?

Your science class launches a model rocket from the ground. The model

rocket is launched upward with an initial velocity of 128 feet per second.

The acceleration due to gravity is 32 feet per second squared.

2. Write an equation to model the distance the rocket travels. Let d be the distanceand let t be the time in seconds.

3. How high will the rocket be after:

a. 1 second?

b. 3 seconds?

Chapter 3 ● Assignments 55

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Name _____________________________________________ Date _____________________

Assignment for Lesson 3.1

3

c. 4 seconds?

d. 6 seconds?

e. 7 seconds?

4. Use the information from Questions 1 and 2 to complete the table.

56 Chapter 3 ● Assignments

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3Time Height

t

1

3

4

6

7

Quantity Name

Unit

Expression

Name______________________________________________ Date _____________________

5. Use the table in Question 4 to graph the height of the rocket versus the time.

6. Use the graph to approximate the maximum height of the rocket and the amount oftime it takes for the rocket to reach its maximum height.

7. Use the graph to approximate the amount of time it takes for the rocket to reachthe ground.


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Intercepts, Vertices, and Roots

Quadratic Equations and Functions

For each quadratic function, complete the table and graph the function.

On the graph, label the y-intercept, x-intercept(s), and vertex.

1. 2. y � x2 � 2xy � x2 � 4x


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Assignment

Name _____________________________________________ Date _____________________


3x y

�5

�3

�2

0

1

x y

�2

�1

1

3

4

3. 4.

Determine the roots of each quadratic equation by factoring.

5. 6.

7. 8. 3x2 � 27 � 0x2 � 25 � 0

12x � 4x2 � 0x2 � 10x � 0

y � �x2 � 6x � 7y �12

x2


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x y

�3

�1

0

2

4

x y

�1

0

1

4

7

Name______________________________________________ Date _____________________

9. 10. x2 � 6x � 5 � 0x2 � 4x � 4 � 0


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Quadratic Expressions

Multiplying and Factoring

Calculate the product.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Factor the expression.

10. 11. 12.

13. 14. 15.

Determine the zero(s) for the function.

16. 17. 18.

19. 20. 21. x2 � 11 � yx2 � 9x � 10 � yy � x2 � 5x � 36

y � x2 � 22x � 121x2 � 13x � 30 � yy � x2 � 8x � 12

16x2 � 15x2 � 9x � 2x2 � 3x � 40

x2 � 12x � 36x2 � 7x � 10x2 � 3x � 4

( x �34 )

2

(�2.4x � 3) (1.1x � 4.5)(2x � 1) (x � 3)

(x � 5) (x � 6)12

x ( 45

x � 3 )0.5x(x � 0.2)

�2x(4x � 1)3x(x � 5)x(x � 7)


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Name _____________________________________________ Date _____________________


3

22. 23. 24. y � 3x2 � 12x � 12y � 8x2 � 82x2 � x � 1 � y


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More Factoring

Special Products and Completing the Square

Calculate the product.

1. 2. 3.

4. 5. 6.

Factor the expression.

7. 8. 9.

10. 11. 12.

Solve the equation by completing the square.

13. 14. 15. x2 � 8x � 3 � 0x2 � 10x � 5 � 0x2 � 6x � 2 � 0

4x2 � 12x � 925x2 � 169x2 � 1

x2 � 9x2 � 16x � 64x2 � 2x � 1

(x � 10)2(x � 6)2(x � 15) (x � 15)

(x � 12) (x � 12)(x � 9) (x � 9)(x � 7) (x � 7)


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3

16. 17. 18.

19. 20. 21. x2 � 15x � 9 � 0x2 � 3x � 1 � 0x2 � 14x � 18 � 0

x2 � x � 7 � 0x2 � 4x � 2 � 0x2 � 20x � 40 � 0


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Quadratic Formula

Solving Quadratic Equations Using the Quadratic Formula

Solve the equation by Using the Quadratic Formula.

1. 2. 3x2 � x � 2 � 0x2 � 21x � 108 � 0

3. 4. x2 � 7x � 20 � 0x2 � 21 � 0


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3

5. 6. 6x2 � 5x � 03x2 � 2x � 1 � 0

7. 8. �3x2 � 6x � 2 � 0x2 � 2.2x � 0.85 � 0


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Name______________________________________________ Date _____________________

9. 10. 2x2 � 10x � 11 � 04x2 � 5x � 1 � 0

11. 12. 3x2 � 31x � 36 � 0�6x2 � 6x � 180 � 0


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Graphing Quadratic Functions

Properties of Parabolas

Complete the table and graph the quadratic function. Identify the vertex,

x-intercept(s), y-intercept, and axis of symmetry.

1.

vertex: ____________

x-intercept(s): ____________

y-intercept: ____________

axis of symmetry: ____________

2.

vertex: ____________

x-intercept(s): ____________



y � x2 � 2x � 8

y � x2 � 4x


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Name _____________________________________________ Date _____________________


3x y

�4

�3

�2

�1

0

x y

�2

0

1

2

4

3.

vertex: ____________

x-intercept(s): ____________



4.

vertex: ____________

x-intercept(s): ____________



Consider the equation of a parabola where a, b, and c are

real numbers, and a is not equal to zero.

5. Describe the graph of when a is positive.y � ax2 � bx � c

y � ax2 � bx � c,

y � �x2 � 5x � 6

y � �13

x2 � 3


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x y

�6

�3

0

3

6

x y

�7

�6

�2

0

1

Name______________________________________________ Date _____________________

6. Describe the graph of when a is negative.

7. Describe the graph of when c is positive.

8. Describe the graph of when c is negative.y � ax2 � bx � c

y � ax2 � bx � c

y � ax2 � bx � c


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Graphing Quadratic Functions

Basic Function and Transformations

Describe the transformation(s) of the basic function that produces

the graph of each given function, where a is a positive integer.

1.

2.

3.

4.

5.

6. y � �1a

x2

y �1a

x2

y � �ax2

y � ax2

y � x2 � a

y � x2 � a

y � x2


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Name _____________________________________________ Date _____________________


3

9. 10.

Vertex: __________ Vertex: __________

y � �2x2 � 12x � 10y �14

x2 � 3x � 9


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Determine the vertex of the given function. Then graph the function and

describe the transformations of the basic function that produce the

graph of the given function.

7. 8.

Vertex: __________ Vertex: __________

y � x2 � 8x � 15y � x2 � 6x � 5

y � x2

Three Points Determine a Parabola

Determining Quadratic Functions

Determine the equation of the parabola that passes through the three given

points.

1. (�1, 12), (1, 2), (2, 0)


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Name _____________________________________________ Date _____________________


3

Name______________________________________________ Date _____________________

4. (�2, 1), (�1, 2), (0, 5)

5. (6, �7), (�4, �2), (6, 0)


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Time to Discriminate

The Discriminant and the Nature of Roots/Vertex Form

Use the discriminant to determine whether the function has one real root,

two real roots, or no real roots. Then determine the root(s), if possible.

1. 2.

3. 4.

5. 6. y � 3x2 � 4x � 9y � �5x2 � 3x � 7

y � x2 � 9y � 3x2 � 246

y � 16x2 � 24x � 9y � 2x2 � 2x � 24


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3


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Write each function in vertex form. Then determine the vertex.

7. 8.

9. 10.

11. 12.

Determine the vertex and then graph the function.

13. 14.

Vertex: ____________ Vertex: ____________

y � �( x � 1)2 � 8y � ( x � 4 )2 � 2

y � 4x2 � 48x � 147y � �x2 � 6x � 3

y � 5x2 � 40x � 79y � �3x2 � 12x � 7

y � 2x2 � 4x � 6y � x2 � 10x � 15

17. 18.

Vertex: ____________ Vertex: ____________

y � 3(x � 2)2 � 3y � �0.5(x � 7)2 � 4

Name______________________________________________ Date _____________________

15. 16.

Vertex: ____________ Vertex: ____________

y �13

(x � 6)2 � 7y � 2(x � 3)2 � 1


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assignment · 2010. 8. 20. · lots and rockets introduction to quadratic functions 1. the length...

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